Scalloped beam amplification



April 8, 1958 T G, MlHRAN 2,830,223

SCLLOPED BEAM AMPLIFICATION Filed April 22, 1954 l v 5 Sheets-Sheet 1INVENTOR, Theodore G. Mihran,

His. Attorney.

April 8, 1958 T. G. MIHRAN 2,830,223

scAL'LoPED BEAM AMPLIFI'CATION Filed April 22, 1954 s sheets-sheet 2 IINVENTOR Theodore G Mihrjan,

April 8, 1958 T. G. MIHRAN 2,830,223.

SCALLOPED BEAM AMPLIFICATION The odore Ml'hran,

BY J d@ His Attorney.

United States Patent 2,830,223 scALLoPEn BEAM AMPLIFICATION Theodore G.lMlihran, Schenectady, N, Y., assignor to General Electric Companyacorporation of New York Application April 22, 195e, Serial No. 424,918 1Claim. (Cl. 31E-5.35)

This invention relates to an apparatus vfor amplifying high frequencyelectromagnetic signals.

My invention is ydirectedto ya continuous interaction devicewhich-amplies a radio frequency signal applied to an electron beam, thediameter of which varies periodical'ly to define successive regions ofvarying direct current density. Amplification is obtainedl byinteraction of the modulation produced by the radio frequency signalvoltage and the beam of varying diameter. This mechanism ofamplification is relatively insensitive to wide swings in operatingfrequency. My invention is essentially independent of boundaryconditions; that is, a signal can be applied to a control grid, avelocity modulation cavity orV a helix in order ,-to modulate and vary.the axial radio frequency electron density in an 'electron beam. Such anelectron beam can be caused; to traverse a eld free drift space orregion andbe collected by a conventional energy extracting apparatus.vBy .properly selecting the strength of the magnetic field inthe fieldfree drift space and the position of the electron :source to properlyshape the beam, amplification in the field free drift space may berealized. Therefore, amplification is accomplished without the necessityof an accompanying physical circuit which renders conventional electronbeam amplifying apparatus mechanically more 'complex and less eiicient.Itis, therefore, an object of my ,invention to provide an apparatus forVampli'- fying electromagnetic venergy which is independent of anyinteraction .of the electron beam with an external structure.

It is a further object of my invention to'provide an apparatus foramplifying :electromagnetic energy which is relau'vely insensitive to=variationsin the `frequency of the electromagnetic energy to `beamplified.

Another object of my invention is to provide Van ap'- paratusfoi-amplifying electromagnetic energy whereby the amplification takesplac in a eld free `drift region.

Itisqan object of my invention to'provide `any apparatus which isadapted to amplifyelectromagnetic energy at short wavelengths. t

It is also anobject of .my invention topi-Ovide an apparatusto amplifyan appliedsignal by interaction of the signal with an electron -beam ofvarying diameter.

.An amplifier in accordance with my invention may consist of an electrontube structure comprising an electron gun for producinga stream, ofelectrons. The electron stream is first accelerated and then caused topass through an equipotential region or field free drift space to acollector electrode; A magnetic beam shaping field is provided to formthe stream of electrons in the eld free drift space into successiveregions of Varying direct current electron density.V The Yelectronstream isrmodulated by a radio 'frequency signal to Vform electrongroups or bunches in the electron stream. The bunches are then properlyoriented with'respect to 'the regions of varying '0 'l 2,830,223v,Patentetl Apr. 8, 1958 Yand-beam'diameteras' va function ofdriftdistance from ,the

Cafhde il allemal appartusinccrporatmsmy inventiqn; Figures 6 and 7illustrate structure incorporating my 1nvention.

In order to describe my invention,i t willbe necessary from ,timen to,time t-o refer to termsandphenomena which will .be described 'in theimmediate succeeding paragraphs inthe form of definitions.

Referring now to Figure l of the drawing there is illustrated athermionic cathode 1, which emits electrons, a control electrode v2, anaccelerating.electrode 3,a magnetic shield 4, a movable output cavity Swith 'electron perme-` able members'o 'and`7 and output coupling meansSuitable voltages are applied to the accelerating .electrode so thatelectrons 'Vemit'tedbyV the cathode travel alongvthe lin indicatedbythewordfbeani. andare collected by collectorf91'. Output cavity 5 can beadjustedV autiallyv along the electron beam. The magnetic'shieldjhlacceleratig electrode 3, movable output cavity -5 andcollector9're maintained at the same direct current. potential.Therefore, the region from 'accelerating electrode 3 t-o collector 9 maybe considereda field free drift space, i. e. no direct currentaccelerating potential is applied to anclcftiion in the beam vonce itleaves accle'ratirigI lectrode 3-ah4`d` travels to collector 9. Amagnetic eld is provided having flux owing in thedirection. indicated bythe arrows H. Magnetic Ishield 4 is maintained at the same directcurrent` potential .as eelectr'ode 3 'andals'o prevents any magneticlinx from ,alfec'ting'the-1fcathode and control grid. If a radiofrequency signalisapplied between cathode 1V and grid 2, a densitymodulation ofjthe.electrons in an axial direction results. f

, yYl/ithfthe` above brief'description of lFigure'rl the Y plasmawavelengthmay :bedened The application oa radio frequencysignal betweenelectrode 2 and cathode 1 results in a-va'riation-in the electronVdensity in an axialV posed uponV the beam of lectrons traveling fromcathode 1tocollector9. ,p pl i *A These variations in the-axial electronconceiltiati'oninayV be considered as groups or bunches-which areseparated by a distance which is definedas anjelectron wavelength, i. e.if no degrouping or debunching forces are present due to the naturalrepulsive elfectspof particles with like charge, a series of bunchestravels dowrnthe beam between accelerating electrode 3 and collector 9.The distance between these bunches is Adetermined by the frequency oftheapplied modulating s'ignal voltage and ythe -direct current beamvelocity. Actually the bunches tendtodisperse due to naturalrepulsionforcesv so that katfsome point along thebeam the electrons in any given,bunch leaving the accelerating electrode 3 are completely debunched andhave a maximum axial velocity. This distance between a group V'ofelectrons which are completelyrbunched and the `same group whencompletely debunched is defined as one-quarter plasma wavelength. Thisplasma wavelength 3 I and, in the one dimensional case to be describedbelow, is completely independent of modulating frequency. Plasmawavelength may also be defined in terms of a mathematical expression, aswill be given below, and also in terms of physical phenomena as twicethe distance vbetween two regions of maximum for minimum electronconcentration.

The plasma frequency must first be derived for the conf ditionwhereinthe natural tendency of electrons toV repel where e and m are thecharge and mass respectively of an electron, e is the dielectricconstant of free space, i0 is current density in amperes per squaremeter and uo is the direct current velocityof the charges. The directcurrent velocity is that velocity given to an electron by the electricfield between the cathode 1 and the accelerating .grid 3. Equation l maybe rewritten in terms of the plasma frequency so as to read i The periodof theplasma oscillation is equal to the reciprocal of the frequency,therefore Gulli-5 ,.(3)

The wavelength isjequalto the velocity times the'period; thereforeAp=uuTp or substituting from Equation 3 When the beam is cut down to afinite size, i. e. the crosssection thereof is of finite size, theplasma frequency is lowered due to arelative weakening of the axialelectron forcesl which is caused by the diversion of a portion of therepulsion forces in directions other than along the beam axis. Theeffective plasma frequency can therefore be defined as fq where l A Yf.=[F1f`,`where F 1 (5) and il (6 A f [F1 P l F is afunc'tion of p y i i(beam diameter) 'd i t (tube diameter) an 7d where i -.d u #o (7) andwhere f is equal to the modulating frequency or frequencyof the signalto beramplifed. It is noted `that the function F is affected byvariations in themodulating frequency; however, the effect is relativelysmall, especially if the beam diameter or the modulating frequency islarge.

Before discussing'somerof the methodslofobtaining a beam.A ofcyclically'varying diameter .defining successive regions of highk andlow direct current electron density which is `referred to in thisspecification as a scalloped beam, it will be necessary to define the'action of an elec-v tron `in a magnetic: field.` This definition willinitially de- Vfine electron motion without space charge eects. When anelectron is projected into a magnetic field in a direction transverse tothe lines of fiux it will tend to spiral and will travel through 360 ofsuch spiral at a frequency which is called the cyclotron frequency. Thecyclotron frequency may be defined as where e and mv are the charge andmass respectively of Y an electron and B is the ux per unit area in thedrift space. Expressed in terms of the cyclotron frequency, the aboveequation may be written as and the period may be expressed as 21rm TeeBif Athe electron is projected into the field with a direct currentvelocity un, the electron travels in a helix of con stant diameterandthe axial distance between like por# tions of the helicalpath may bedefined as the cyclotron wavelength andmay be written inthe form of anequation as If space charge effects are takenV into consideration, aportion of the magnetic field is utilized in overcoming the naturalrepulsioneffects of the electrons in the beam and the portion of themagnetic field available to cause the Aelectron to spiral is reduced bya `factor K. Since thefconditions necessary for a scalloped beam includean appreciable space charge effect the scalloped beam wavelength may bedefined as Y (12) where the initial velocityilo may be expressed by theequation f' i 2e f i 'un-Eye (13) and wherer'Vo `is* the direct currentpotential which accelerates the electrons to a velocity un. In apreferred forrngof the apparatus of my inventiomK has a value whichVlies in the range ,from 1 to 0.707. It should be noted that there mustbe a force or velocity componentA ofthe electron ,which is transversetothe electric field in'order to realize spiraling of the electrons atthe scalloped beam frequency. ThisV force or velocity component resultsfrom the natural repulsion effects between adjacent electrons. 4

An example of several methods forobtaining a scalloped bearnmay be`described by `reference to Figures 2a to 2e in which the structure of 2amay be considered the defocusing aperture in magnetic shield 4 throughwhich the electron beam passes. The direction of the magnetic field isillustrated by arrows H. At the'entrance of aperture 4 there is'acomponent of the magnetic field which is perpendicular to the directionof propagation of any one electron e emitted by cathode 1. Such anelectron is indicated by the dot labeled e and the arrow indicates thedirection which e will tend to take if it is projected into the abovedefinedv magnetic field in a direction into andperpendicular to thesurface of the drawing.` The-electron will acquire an angular velocitywhich maybe definedas ws=wcK were ws is thescalloped beam angularvelocity. Y Y Y In order to produce av scalloped beam certain criticalstartingconditions are necessary. `It may now be as*- sumed thatelectrons leave a Vcathode that is magnetically Shielded vandaresuddenly introduced intoa magnetic field 'by means of a 'defocusingaperture in a magnetic shield and accelerating anode .as illustrated inFigureZ'c. In going through the fringing yportion .of the magneticfield, the electrons acquire an angular velocity as has been previouslydescribed, VVwhich interacts with the uniform portion of the magneticifield present in the drift space and produces an inward force on theelectrons. With a proper choice of magnetic 'field strength B, thisforce can be made to cancel exactly the outward spacecharge andcentrifugal forces of lthe beam. Under 'these conditions all electronstravel down the beam in helices about the axis of symmetry and theoutline of the beam s smooth as shown in Figure 2c. It is noted that thedefocusing Vaction of the aperture must be taken into account in orderto present a parallel electron beam to the magnetic field.

There is a definite relation Vbetween the beam current I0, the beamvoltage V0, vthe magnetic field strength B,- and the beam radius .rewhich must be satistield in order to obtain a beam having this smoothoutline. This relationship may be developed in accordance with equationsand phenomena well known in the art to render an expression in terms ofmeterkilogramsecond units known as the conditions necessary for what iscustomarily termed Brillouin flow. This relationship -may be expressedin the form of Equation l4.

I:l.45 l06B2V01/2re2 (14) Not only must this relationship hold, but theelectrons must enter this region in essentially parallel flow, i. e.traveling in a direction parallel to the beam axis and at a radius re.If these conditions are not fulfilled the electrons tend to deviate fromthe equilibrium radius.

One method of obtaining a scalloped beam is by introducing the electronsin a non-parallel electron beam such as illustrated in Figure 2d. Figure2d shows an electron gunwith a given angle of electron beam lconvergencewhich is placed behind an aperture with a different defo'cusing angle sothat the electrons in 'the beam tend to diverge when introduced into themagnetic field.

It is well known in the art that when an electron beam is projected downa tube having finite dimensions that the force on an individual electrontending to deviate from a parallel path along the beam is at a minimumat the equilibrium radius of the beam. This equilibrium radius has beendefined as re. This force, which tends to return the electron to aposition at rthe equilibrium radius, increases as an individualelectron4 deviates from this equilibrium radius. Therefore, an electronor group of electrons projected through an aperture suchy as theaperture illustated in Figure 2d will be in a potential field thatlimits the radial travel of the electron and tends to return the'electron toward the lequilibrium radius. Uponreaching the equilibriumradius, however, .the elecnon has acquired an inward radial velocity.This causes the electron to overshoot the equilibrium radius and againthe potential field brings it to rest, this time at a radius somewhatless than re. The electron is again returned toward the equilibriumradius and reaches the equilibrium radius with thesame velocity it hadat the beginning of the cycle. The cycle repeats as the electron travelsalongthe beam toward the collector. -In other words, the electronsoscillate about the equilibrium radius. The wavelength of thisoscillation has been previously developed and is den'ed by IEquation l2.

`Another method of obtaining Va scalloped beam is illustrated in Figure2e. In this instance a magneticfield other than that specified inEquation .14 is utilized so that the electron beam has a radius, inthiscase greater than theequilibrium radius re which is defined byEquation 14. This means that 'parallel iiow electrons are being injected-into a magnetic field at a radius other than the equilibrium radius.The electrons are in a potential field and are acted upon -to return tothe equilibrium radius. Upon reaching it, they have acquired kineticenergy which carries them through it toa smaller radius,

and again oscillations take place .about the equilibrium radius and theyresult lis a scalloped beam 'thewavelength of which is defined byEquation l2. Thus a scalloped beam can be obtained With an initialparallel flow vbeam merely bythe use of a magnetic field strength otherthan that given by Equation 14.

The vpotential field which has been mentioned in the above paragraphswhich tends to return electrons on either side of the equilibrium`radius to the equilibrium radius may be better understood 'by applyingthe analogy of a simple pendulum. At the upper vend of the pendulumtravel the energy in 'the pendulum is all in vthe `for'rn o'f potentialenergy. At the bottom end of the :pendulums travel the pendulum hasmaximum velocity and 'Zero vpotential energy. At some intermediate pointin the travel of the pendulum on either side of the bottom dead centerposition the pendulum will possess both kinetic and potential energy.rIf we now substitute 'an electron for the pendulum and assume thelbottom dead center position as the condition at the equilibriumradiusit may be seen that for the above-described intermediate positions ofthe pendulum or electron there will be a force which is composed of bothpotential and kinetic energy which will cause the electron to swingyfrom a region outside to a region inside the equilibrium radius.

It is noted that these are merely a few vexamples of rmanners in which ascalloped beam may be `obtained and that any method ofobtaining ascalloped beam may be used' in the practice of my invention. Forexample, when the cathode is not shielded, i. e. whenthe magneticeld'threads through the cathode, vbeam scalloping will always occur.There lis no critical 'magnetic field to prevent radial motion ofyelectrons in the beam.

VFigures 3 and 4 illustrate the mechanism of my invention. lFigures 3ato 3e illustrate the actionof electrons throughout one-half plasmawavelength in a beam which has a constant'direct current density.r Forthe purpose of this discussion the constant forward velocity p@ isneglected since the effect of this velocitymerely shifts the'illustrated electron distribution tothe right hand side of the drawingat a constant rate. It mustbe understood that the electrons illustratedby .the dots in Figures 3 and 4 are those electrons which are in amaxirnum hunched condition and which are formed by an applied modulatingsignal voltage. These bunches define regions of high radio frequencycurrent density. The

velocity of an electron relative to the direct 'current elect tronvelocity is referred to as radio frequency velocity. 1

It is noted that Figures 3 and 4 do not show those bunches which may bepresent when the electron` wavelength is less ythan the plasmawavelength .and Vthat a completeV illustration would also show othervbunches in various stages of debunching ory rebunching between theillustrated bunches. In the absence of such an applied modulating signalthere would vbe a uniform distribution of electrons present inthe driftspace which would be moving from the left hand side 0f Figure 3 to theright hand side with an average velocity uo as indicated by the ar rowand which are referred to as direct current. The horizontal boundarylines may be Vassumed to define the outer surface or envelope of abeamof uniform direct current density. The dots illustrate bunches ofelectrons which are separated by one-half plasma wavelength and whichmay be formed by any conventional density modulating or velocitymodulating apparatus. There is no direct current potential differencebetween the ends 0f the illustrated electron beams. The phenomena aboutto be described occurs in a field free drift space. The

electrons in these bunches have a natural tendency toV drift apartgiving up their high potential energy whichV they had when in a bunchand converting this potential energy into kinetic energy..r At a timet3, as illustrated in Figure 3c, approximately one-quarter plasmawavelength later, the electrons have given up. all their potentialenergy and are essentially uniformlydistributed along the tube orelectron beam. In this condition it may be assumed that the electronshave `a maximum velocity and that the instantaneous alternating currentis zero. At a time t4 as illustrated in Figure 3d the electrons havestarted to regroup or bunch at a region between the original bunches.-The electrons are then giving up their kinetic energy due to thenatural repulsion forces between the electrons and their velocity isdecreasing while the instantaneous radio frequency current density isincreasing. At a time t5' which is equal to one-half plasma period afterthe initial time t1 the electrons have completely rebunched, haveeffectively zero velocity and the instantaneous radio frequency currentdensity is at a maximum.

In a conventional drift tube amplifier a standing wave of radiofrequency current will be established, very much inthefashion .describedin the analysis of Figure 3'of the drawing. This standing wave will takethe form as illustrated in Figure 4a in which there will be `regions ofmaximum axial electron concentration separated by one-half plasmawavelength and with an intermediate region therebetween at which theelectron concentration is at a minimum and the electron velocity at amaximum. Figure 4b illustrates a beam of electrons the direct currentdensity of which varies rapidly at certain points along the field freedrift space due to a change in beam diameter. Figure 4c illustrates thecurrent and electron velocity characteristics of electrons in a beam thedirect current density of which varies inversely in accordance with thediameter of the envelope of Figure 4b. It may be seen Ythat the maximumelectron density is the same in each of the regions illustrated inFigure 4a. This is because the potential energy given up when theelectrons separate and reach maximum Velocity is completely convertedrinto kinetic energy and the kinetic energy is then completelyreconverted into potential energy in forming the next bunch. Thisanalysis is sound if it is assumed that no other forces are acting onthe electron other than those along a line parallel with the beam axis.

Anunderstanding ofthe term electric restoring force may be had byassuming a region with a given average number of Ielectrons per unitvolume. lf a series of bunches or groups of electrons are suddenlyintroduced into this region the electrons in each bunch will immediatelystart to separate or debunch due to the natural repulsion effects ofparticles with like charge. The electrons in the4 bunches will `tend toform new bunches as has been described in regard to theV illustrationsof of Figs. 3a to 3e. The force tending to debunch the electrons is afunction of the average electron concentration in the region as well asthe radio frequency electron concentration. If we now assume a fixedinitial radio frequency electron density in the bunches, the electricrestoring force will be proportional to the direct current electrondensity only. lf the given average number of electrons per unitvolume isincreased, the tendency of the electrons to debunch is increased and thetendency to bunch is decreased. If the direct current electron densityis decrease the electrons have less tendency to debunch and converselyelectrons traveling toward each other with a given velocity will tend toform a tighter bunch. For purposes of this specification, a region oflow direct current electron density is termed a region of low electricrestoring field, i. e. the tendency of the electric field to slow downelectrons having a given velocity is low-so that highly concentratedbunches of electrons are formed. Conversely a region of high directcurrent electrondensity is said to have a high electric restoring field.Y

Referring now toFigures 4b and 4c it will be assumed that a currentmaximum occurs. in region A. It should be noted that the currents andvelocities herein mentioned are instantaneous or alternating currents asdistinct from the directcurrent component of the beam. As a radiofrequency signal bunch in region'A progresses toward region B,ldebunching forces will gradually convert the potential energy of thebunch into kinetic energy.` Onequarter of a plasma wavelength later atpoint b there is a current null and a velocity maximum.V If the direct.current density is reduced suddenly at this point as is illustrated inFigure 4b by the expanded envelope of the direct current beam, the radiofrequency or alternating` current velocity of the electrons remainsunchanged and as further drifting occurs the kinetic energy of the electrons is gradually reconverted into potential energy. However, becauseof the reduced direct current density in region B and resulting reducedelectrical restoring force when the electrons reach a current maximum atpoint c they arecloser together axially than they were at point a. ltshould be noted that with the reduced direct current density and reducedelectric; restoring or debunching force the electrons drifted furtherbefore giving up all of the kinetic energy and reaching a point ofmaximum concentration. The electrons at point c are more tightlycompressed than at point a, and constitute an increased total radiofrequency current in the beam. At point c the direct current density canbe returned to its initial value without altering the total radiofrequency current in the beam. No energy is expended in reconcentratingthe beam, since, for the purpose of this analysis, only the repulsioneffects along an axis parallel with the beam axis are being considered.It is further noted that where the electron wavelength is less than thebeam radius the repulsion or fringe effects perpendicular to the axis ofthe beam are relatively low and, therefore, this theoretical assumptionthat no energy is required to increase the direct current density of thebeam is substantially accurate.

However, in an apparatus having finite dimensions,

energy is extracted from the electron beam in reconcen-Y trating thebeam. This energy is transferred to the radio frequency field andcontributes to the observed gain.

It may therefore be seen that the radio frequency current in an electronbeam can be enhanced by arranging to have high direct current density inthe region of the beam where debunching occurs and low direct currentdensity where rebunching occurs. This processmay be repeated for as manycycles as desired along the drift space and will result in anexponential growth of the currentstanding wave maxima.

In actual practice it is not possible to achieve a per` fectly steppedbeam of varying diameter defining regions of varying direct currentdensity in accordance with the steps shown in Fig. 4.v `However,V ithas` been found that veryV similar results may be obtained by using ascalloped beam which is produced in the manner previously described. Foroptimum gain, the scallop wavelength should equal one-half the plasmawavelength. This is in agreement with the description of Figure 4, sincethe condition illustrated in Fig. 4 would occur when the scalloped beamapproximates most nearly the ideal stepped beam.l Furthermore, the smalldiameter section of the scalloped beam should coincide with thedebunching portion and the large diameter section with the rebunchingportion of the standing wave of radio frequency current. That is, 'theradio frequency current null should occur when the beam diameter is nearits equilibrium value and increasing. This phase relationship isexhibited clearly in Figure 4c.

A typical curve is illustrated in Figure 5 of the drawing. The solidcurve shows a standing wave of power output, the maximum amplitude ofwhich increases exponentially with distance. This curve was taken with asliding cavity apparatus similar to that illustrated by Figure 1 of thedrawing. The current Wave was initiated by a space charge controlsection operating at 1000 megacycles. A radiofrequencysignalsof-1000inegacycles Wasapplied Abetween the control electrode 2andcathode 1 to density vmodulatef-the electron beamfowing from cathode1 through the. eld free. drift'spacey to 4collector 9. iThe..outputpower was measured with-amovable cavity such ascavity .5 of `Figured.The`distance of the cavity from the cathodel could bevariedwfrom l -centimeter to25.8 centimeters. The direct Ycurrent beam voltage wasset at500- volts-andthe `cathode current at 50 rnilliamperes. Undertheseconditions again of 13.4 'decibels was observed Vwith the cavitysnug against the accelerating anode. As the cathode to-output1cavitydistance wasincreased a'standing wave ofV outputpower was obtained witheach successive maximum' several decibels above the maximum ofthepreceding wave. 'i

`Vith the cavity placed 25.8 centimeters from thefcathode, ar'nvoverallgain of 24.0 decibels was A"measured, of which 10.6 decibels was due tothe scalloped beam amplification phenomena. *DuringVthesemealsureme'nts, the magnetic field was held Lconstant at V.92ga`i1ss.- The Edotted 'curve of lFigure 5 shows how the YdiameterYo'fthejbeam varied along the drift space under these conditions. `'Itshould be noted that corresponding to thefiive lAhalf "plasmawavelengths of radio frequency'power, therefare ve scallops in the beam.A;halfplasma-'wavelength is the distance from one radiofrequencyVcurrent minimum to another radio frequency currentminimum. It shouldalso lbe noted that the phasingbetweenthe plasma wave and the directcurrent scallops is very close 'to the optimum phasing `developed in thediscussion of Figure An idearof ;the;gain thatvcan be expected from thisphenomena maybe obtained by amathematical analysis of Figure 4c in whichthe amplitudes of the velocity and current densityfwaves which existinvthe ybeatnmay be dened by equations In these equations VA is theinstantaneous radio frequency or alternating current velocity of anelectron at any point in region A; vb is the radio frequency oralternating current velocity of an electron at the beginning of region Band is also the maximum electron velocity; uo is equal to the directcurrent or average electron velocity; iA is the instantaneous radiofrequency or alternating current density in region A; wqA is theeffective plasma radio frequency in region A, IdA is the direct currentdensity in the same region and Z is the distance along the axis of thebeam. Boundary conditions may be established by assuming that at point-a It should be noted atl this point, `that the 'values1 Igiven for vaand in are absolute values and that in orde'rztozcarry gut; thisanalysis,l a boundary conditionrmust-.be-selected 'Z wqAu-o which willrender the velocity zero v'at Vpoint a. `It is further noted that this`analysis lis vbased yon, the onerdim'ensional action of the electronsalong the Z axis krirbeam axis onlyand that finite beam size is takeninto a"cco`unt by theuse'of the effective plasma frequency rather thanthe one'dimensional vplasma frequency. It may Ybe Iassumed that thesignal bunch willdrift until y,the current density modulation iscompletely convertedfinto .velocity modulation at point b. -At thispoint Vthe magnitude of the-radio.- frequency velocity i's simply vbandthe radio frequency current density is `zero since lidi:

By "expanding the beam the current density is reducedto IdB which.' isthe-direct current densityin the B region of Figure 4c. This does notchange the radio frequency velocity at this point but it doeschange theeffective plasma frequency in region B. Therefore, the vcurrent densitywave inthis region'is given by the equationif this current densitywave'is allowed to drift `a quarter; plasma-wavelength to point c itwill reach a maximum value of v Y ici :Uhm-GB To (22) It isconvenient toreturn the direct current beam density toits original yvalue at thispoint since this lmay be done without altering the total radio frequencycurrentin the beam.

The total radio'frequency current is the product of thelra'diofrequencycurrent density and the beam area.

lIf the total radio frequency current at point cis compared to that atpoint a it will be found that the ratio of the currents may be expressedby lcaLAlgaL K T; wq Ida da v where 'dA-and dB are the vbeam diametersYin regions A `and yB respectively. The effective plasma frequency wq isgivengby the equationV Y Current gain- FB A Power gain is proportionalto the square of the current gain and may be written in equation form asFB di db Although Equation 27 Agives the power gain for the stepped beamof Fig. 4b, it may readily be seen that it I Power gain=20 logro l 1also gives an upper limit for gain when a scalloped beam is used. f Y

Figures 6 and 7 illustrate two types of apparatus incorporating myinvention. Figure 6 illustrates an amplifier utilizing densitymodulation and constructed in accor'clance with my invention andFigure 7illustrates an amplifier utilizing velocity modulation and constructedto permit practice of my invention. Like components in each of thesetwo'figures are designated by the same reference numerals. y

Figure 6 illustrates a densitymodulated drift tube structure with acathode 10 including a heater element 11 supported in tube 12 by glassbeads 13. Tube 12 has a fine 'wire grid 14 across the end thereof and isconstructed so that ahigh frequency signal may be applied between thecathode structure 10 and the tube 12. Tube 12 is supported by disk 15and annular insulator 16. The complete assembly is mounted onmagneticshield 17. Power supplyY 18 Vprovides current for heater 1,1,`source 19 provides grid bias for grid 14 and power supply 20 provides adirect current potential between cathodel and accelerating grid 21. Atube 22 of stainless steel is mechanically -and conductively coupled tothe magnetic shield 17. Tube 22 is provided at the end thereof with atunable output cavity 23 which maybe constructed of sheet copper. Cavity23 is provided with grid structures 24 and 2S, a copper collector 26,and an output line 27. Tube `22 defines the field free drift space orregion and is maintained, as is the restof the structure from magneticshield 17 to output cavity 23, at the same direct current potential.Therefore, there lis no directvcurrent potential difference between theaccelerating grid 21, and collector 26. Solenoid 28 lsurrounds thedrifttube 22 and when energized by'power supply 29, provides aunidirectional magnetic field withinlthe'drift tube in the directionillustrated by the arrows yI-I.

Figure 7 illustrates a structure which is similar to that illustrated inFigure 6 except that velocity modulation is utilized to produce bunchesof electrons in the electron beam. Tunable. cavity 30 consists of ametal ch-amber with grids; 31 and 32 and input lead 33. It is noted thatthere is no control `grid as in the structure of Figure 6. The`apparatusfillustrated in Figure 6 is operated by connecting the powersupplies 18, 19 and 20 to the tube structureso as` to produce a beambetween c-athode 1 and the collector 26. Thepower supply forsolenoid 28is then adjusted to produce a scalloped beam.. A scalloped l beam beingconsidered to bewone the diameter of the outer envelope of which variesperiodically between the accelerating grid 21 and the collector 26. Themagnetic field is adjusted'so that accelerating grid 21 andthe entranceinto the output cavity.V 23 will be located where the beam has anequilibrium diameter andy wherethe beam is contracting. This is aninitial adjustment of the scallops on the beam. A high-frequency signalis then applied to Lthe input of the tube to produce avarying fieldbetween cathode r1l) andV control grid` 14. This will produce densitymodulation in the electron beam. The magnetic liux is then varied byadjusting solenoid power supply 29 to produce scallops in proper phaserelationship l 2 to the density modulation. The apparatus of Figure 7 isoperated in asimilar fashion. .In the case of the ap'- paratus of Figure7 the modulator cavity 30 is placed at -a point on the scalloped beamwhere the beam is at the equilibrium diameter and increasing in size, i.e. at a point where the direct current density is at an average valueand the density is decreasing.

It will be readily appreciated that the illustrated apparatus of Figures6 and 7 is given merely by way of example and that any method ofproducing a density or velocity modulated wave on an electron stream maybe used in conjunction with the practice of my invention. Theamplification is obtained by the interaction of the direct current beamand the modulated signal thereon Yandis not dependent upon interactionof a physical struc- -ture with the beam. In the practice of myinvention it has been found that the phenomena accompanying it isrelatively insensitive to frequency variations. An amplifier constructedin accordance with my invention will operate satisfactorily withfrequency variations of as much as two to one. This wide band operationis accomplished by proper adjustment of the magnetic field and theprovision of wide band input and output coupling circuits.

It mayV be readily appreciated that the method and practicev of myinvention may be applied -to innumerable structures and therefore I aimin the appended claim to cover all variations in structure andapplication which fall within the true spirit and scope of the foregoingdisclosure.

What I claim as new and desire to secure by Letters Patent of the UnitedStates is:

A high frequency electron beam amplification system comprising a sourceof electrons, means for accelerating electrons emitted by said source toprovide an electron beam and means spaced from said source forcollecting the electrons and establishing the path of said beam along adrift space substantially free from electric field, means establishingamagnetic field coupled with the beam path and having a directionsubstantially parallel to the beam p ath and an intensity correlatedwith the entrance conditions of the beam to the drift space, the averageaccelerating voltage `and the average current density of the beamV toprov-ide a scalloped beam having a scallop wave length substantiallyequal to one-half the plasma wave length at Vthe frequency of the signalto be amplified, modulating means coupled to the beam near the endthereof adjacenty the source of electrons and positioned to produce aplasma wave having a minimum value located at a point of average vandincreasing' radius of said scalloped beam, and output means coupled tosaid beam at substantially the maximum amplitude of the plasma Wave.

References Cited in the file of this patent UNITED STATES PATENTS RichAug. 24, 1954

